R Notebook

library(tidyverse)
library(plotly)

load("wireless.rda")
wireless_feature = wireless[,3:7] %>%
  mutate(d_S1 = apply(wireless[,1:2], 1, function(x){sqrt(sum((x - as.numeric(AP[1,]))^2))})) %>%
  mutate(d_S2 = apply(wireless[,1:2], 1, function(x){sqrt(sum((x - as.numeric(AP[2,]))^2))})) %>%
  mutate(d_S3 = apply(wireless[,1:2], 1, function(x){sqrt(sum((x - as.numeric(AP[3,]))^2))})) %>%
  mutate(d_S4 = apply(wireless[,1:2], 1, function(x){sqrt(sum((x - as.numeric(AP[4,]))^2))})) %>%
  mutate(d_S5 = apply(wireless[,1:2], 1, function(x){sqrt(sum((x - as.numeric(AP[5,]))^2))}))

plot(x=wireless$x, y=wireless$y)
points(x=AP$x,y=AP$y, col="red", cex=1)

# exploring relationship between distance and signal strength
# without the loss of generality, use X
ap1 = as.numeric(AP[1,])
distances = apply(wireless[,1:2], 1, function(x){sqrt(sum((x - ap1)^2))})
par(mfrow=c(2,2))
plot(y=(distances[distances < cutoff])^2, x=-wireless$S1[distances < cutoff])
plot(x=log(-wireless$S1[distances < cutoff]), y=2*log(distances[distances < cutoff]))

plot(y=distances[distances < cutoff], x=-wireless$S1[distances < cutoff])
plot(x=log(-wireless$S1[distances < cutoff]), y=log(distances[distances < cutoff]))

mod = lm(wireless$S2~log(distances2))
summary(mod)

TODO: try to do that for S2, S3… as well

# exploring relationship between distance and signal strength
# without the loss of generality, use X
ap2 = as.numeric(AP[2,])
distances2 = apply(wireless[,1:2], 1, function(x){sqrt(sum((x - ap2)^2))})
par(mfrow=c(1,2))
plot(y=distances2, x=wireless$S2)
plot(x=distances2, y=-wireless$S2)

cutoff = 100
sample_size = 40
num_iter = 1000

k_s = numeric(num_iter)
r_s = numeric(num_iter)
for (i in 1:num_iter) {
  temp_indices = sample((1:254)[distances < cutoff], sample_size)
  temp_mod = lm(wireless_feature[temp_indices ,1]~distances[temp_indices])
  k_s[i] = temp_mod$coefficients[2]
  r_s[i] = summary(temp_mod)$adj.r.squared
}
mean(k_s)

[1] -0.421104

mean(r_s)

[1] 0.8751914

# using bagging to find the coefficients, using 40 points 
k_s = numeric(num_iter)
for (i in 1:num_iter) {
  temp_indices = sample((1:254)[distances2 < cutoff], sample_size)
  temp_mod = lm(wireless_feature[temp_indices ,2]~distances2[temp_indices])
  k_s[i] = temp_mod$coefficients[2]
}
mean(k_s)

[1] -0.4250205

plot(x=(distances2)[distances2 < cutoff], y=-wireless$S2[distances2 < cutoff])
#for distance above 100, the linear relationship between signal and distance breaks
#lots of points have -92 the worse signal ever 

k = -0.42
d = apply(AP, 1, function(x){sqrt(sum((x - wireless[107,1:2])^2))})
dxy = t(apply(AP, 1, function(x) {as.numeric(wireless[107,1:2]) - x}))
ds.dxy = apply(dxy, 2, function(x) as.numeric(k * x / d))
ds.dxy

              x           y
[1,] -0.1784933 -0.38018434
[2,]  0.3837247 -0.17074941
[3,]  0.4188134  0.03154903
[4,] -0.4035757  0.11630423
[5,]  0.3511401 -0.23043571

ds = wireless_feature[86,] - wireless_feature[107,] 

k = mod1$coefficients[2]
b = mod1$coefficients[1]
signals = wireless_feature[224,]
test = t(apply(AP, 1, function(x) {as.numeric(wireless[224,1:2]) - x}))
test2 = apply(test, 2, function(x) as.numeric(k^2/(signals - b)) * x)
df_mod = lm(as.numeric(wireless_feature[223,] - wireless_feature[224,])~0 + 
                         test2[,1] + test2[,2])
summary(df_mod)

Call:
lm(formula = as.numeric(wireless_feature[223, ] - wireless_feature[224, 
    ]) ~ 0 + test2[, 1] + test2[, 2])

Residuals:
      1       2       3       4       5 
 0.2441  5.0087  1.8471 -0.5603  2.8118 

Coefficients:
           Estimate Std. Error t value Pr(>|t|)
test2[, 1]   -1.643      2.177  -0.755    0.505
test2[, 2]   -2.593      5.225  -0.496    0.654

Residual standard error: 3.501 on 3 degrees of freedom
Multiple R-squared:  0.1827,    Adjusted R-squared:  -0.3622 
F-statistic: 0.3353 on 2 and 3 DF,  p-value: 0.7389

##exploring using differentials 
##

sample_index = sample(1:nrow(wireless), 1)
sample_point = wireless[sample_index,]
sample_diff = data.frame(t(apply(wireless[-sample_index,], 1, function(x) x - as.numeric(wireless[sample_index,]))))
sample_diff_y = sample_diff[sample_diff$y == 0,]

mod = lm(x~.-y, data=sample_diff_y)
summary(mod)

basic_x = lm(x~.-y, data=wireless)
basic_y = lm(y~.-x, data=wireless)
#summary(basic_x)
#summary(basic_y)
avg_error = mean(sqrt((wireless$x - basic_x$fitted.values)^2 + (wireless$y - basic_y$fitted.values)^2))
avg_error

[1] 17.20438

plot(wireless$x, wireless$y)
points(basic_x$fitted.values, basic_y$fitted.values, col="red")
segments(wireless$x, wireless$y, basic_x$fitted.values, basic_y$fitted.values, col="blue")

n = nrow(wireless)
#train_percent = 0.6
#sample_indices = sample(1:nrow(wireless), train_percent*n)
knn_predictions = numeric(n)
pwdistances = as.matrix(dist(wireless[,3:7]))
for (i in 1:n) {
  knn_predictions[i] = (1:n)[-i][which.min(as.matrix(pdist::pdist(wireless[,(3:7)][i,], wireless[,(3:7)][-i,])))]
}

knn_x = wireless$x[knn_predictions]
knn_y = wireless$y[knn_predictions]
par(mfrow=c(1,2))
plot(density(sqrt((wireless$x - knn_x)^2 + (wireless$y - knn_y)^2)),
     main = "knn performance")

#plot(density(sqrt((wireless$x - basic_x$fitted.values)^2 + (wireless$y - basic_y$fitted.values)^2)),
#     main = "regression performance")
knn_errors = sqrt((wireless$x - knn_x)^2 + (wireless$y - knn_y)^2)
knn_avg_error = mean(knn_errors[knn_errors < 100])
knn_avg_error

[1] 10.97828

plot(wireless$x, wireless$y)
points(knn_x, knn_y, col="red")

arrows(wireless$x, wireless$y, knn_x, knn_y, col="blue", length = 0.1)

zero-length arrow is of indeterminate angle and so skippedzero-length arrow is of indeterminate angle and so skipped

knn_bad_loc = wireless[knn_errors > 20,] %>%
  mutate(error = knn_errors[knn_errors > 20]) %>%
  mutate(index = (1:254)[knn_errors > 20]) %>%
  dplyr::arrange(desc(error))

error_bar = 15
plot(wireless$x, wireless$y)
points(knn_x[knn_errors > error_bar], knn_y[knn_errors > error_bar], col="red")

arrows(wireless$x[knn_errors > error_bar], wireless$y[knn_errors > error_bar], knn_x[knn_errors > error_bar], knn_y[knn_errors > error_bar], col="blue", length = 0.1)

par(mfrow=c(1,2))
hist(knn_errors)
plot(density(knn_errors))

par(mfrow=c(1,2))
hist(wireless$x[knn_errors > error_bar])
plot(density(wireless$x[knn_errors > error_bar]))

#trying nearest neightbor + trigulation
point_index = 113
point = wireless[point_index,3:7]
point_d = pdist::pdist(point, wireless[-point_index,3:7])@dist
top_three = (1:254)[-point_index][order(point_d)[1:3]]
top_three

[1]  33 125   4

hover_text = apply(wireless_feature[,1:5],1, function(x) paste(x,collapse = "|"))
p = plot_ly(wireless, x=~x, y=~y, name = "receivers", type="scatter", 
            mode="markers", text=paste(1:254, "<br>", hover_text)) %>% 
  add_trace(x=AP$x, y=AP$y, name = "wifi post", mode="markers", text=rownames(AP)) %>%
  add_trace(x=wireless$x[top_three], y=wireless$y[top_three], 
            name = "neighbors", mode="markers", 
            text=paste(top_three, "<br>", hover_text[top_three])) %>%
  add_trace(x=wireless$x[point_index], y=wireless$y[point_index], 
            name = "neighbors", mode="markers", 
            text=paste(point_index, "<br>", hover_text[point_index]))
p

point_index = 113
point = wireless[point_index,3:7]
point_d = pdist::pdist(point, wireless[-point_index,(3:7)])@dist
top_three = (1:254)[-point_index][order(point_d)[1:3]]
neighbors = numeric(5)
for (i in 1:5) {
  neighbors[i] = (1:n)[-point_index][which.min(as.matrix(pdist::pdist(wireless[,(3:7)[-i]][point_index,], wireless[,(3:7)[-i]][-point_index,])))]
}
neighbors

[1]  33 153   9  33   4

dist(wireless[neighbors,1:2])

           33      153        9     33.1
153  38.47077                           
9    54.00000 79.62412                  
33.1  0.00000 38.47077 54.00000         
4    30.30000 59.06683 23.70000 30.30000

5

point

hover_text = apply(wireless_feature[,1:5],1, function(x) paste(x,collapse = "|"))
p = plot_ly(wireless, x=~x, y=~y, name = "receivers", type="scatter", 
            mode="markers", text=paste(1:254, "<br>", hover_text)) %>% 
  add_trace(x=AP$x, y=AP$y, name = "wifi post", mode="markers", text=rownames(AP)) %>%
  add_trace(x=wireless$x[neighbors], y=wireless$y[neighbors], 
            name = "neighbors", mode="markers", 
            text=paste(neighbors, "<br>", hover_text[neighbors])) #%>%
  #add_trace(x=wireless$x[point_index], y=wireless$y[point_index], 
  #          name = "point", mode="markers", 
  #          text=paste(point_index, "<br>", hover_text[point_index]))
  
p

knn_predictions[3]

[1] 37

neighbors = numeric(5)
for (i in 1:5) {
  neighbors[i] = (1:n)[-point_index][which.min(as.matrix(pdist::pdist(1/wireless[,(3:7)[-i]][point_index,], 1/wireless[,(3:7)[-i]][-point_index,])))]
}
neighbors

after analyzing the error, I find that point 243’s signal for AP3 is completely bad comparing to its neighbors, lets check other access points.

Some points, they only f* up on signal from an access point.

set.seed(12345)
sample_indices = sample(1:254, 50)
plot(wireless$x[sample_indices], wireless$y[sample_indices], ylim=c(0, 145), xlim=c(10, 235))
points(knn_x[sample_indices], knn_y[sample_indices], col="yellow")
points((knn_x-df_x)[sample_indices], (knn_y-df_y)[sample_indices], col="red")

segments(wireless$x[sample_indices], wireless$y[sample_indices], knn_x[sample_indices], knn_y[sample_indices], col="blue")
segments(knn_x[sample_indices], knn_y[sample_indices], (knn_x-df_x)[sample_indices], (knn_y-df_y)[sample_indices], col="green")
#segments(wireless$x, wireless$y, knn_x+df_x, knn_y+ df_y, col="green")

par(mfrow=c(1,2))
plot(wireless_feature$S1, wireless_feature$d1, main="ap1 signal to distance")
plot(wireless_feature$S2, wireless_feature$d2, main="ap2 signal to distance")

plot(wireless_feature$S3, wireless_feature$d3, main="ap3 signal to distance")
plot(wireless_feature$S4, wireless_feature$d4, main="ap4 signal to distance")

plot(wireless_feature$S5, wireless_feature$d5, main="ap5 signal to distance")
# maybe normal method for signal < 70
# modeling xlog distance when signal > 70 
plot.new()

plot(y=wireless_feature$S1, wireless_feature$d1, main="ap1 distance to signal")
plot(y=wireless_feature$S2, wireless_feature$d2, main="ap2 distance to signal")

plot(y=wireless_feature$S3, wireless_feature$d3, main="ap3 distance to signal")
plot(y=wireless_feature$S4, wireless_feature$d4, main="ap4 distance to signal")

plot(y=wireless_feature$S5, wireless_feature$d5, main="ap5 distance to signal")

From the first half of the graph, we can see for different AP, the variance spikes at different points.

Looking at the second half of the graphs.
For access point 5, the relationship between distance and signal is very weak, while
others are more stable. This may have to do with AP5 is in the center of the building.

hover_text = apply(wireless_feature,1, function(x) paste(x,collapse = "|"))
p = plot_ly(wireless, x=~x, y=~y, name = "receivers", type="scatter", 
            mode="markers", text=paste(1:254, "<br>", hover_text)) %>% 
  add_trace(x=AP$x, y=AP$y, name = "wifi post", mode="markers", text=rownames(AP))
p

kclusters = kmeans(wireless[,3:7], 5)
#kclusters$cluster

ggplot(data=wireless) +
  geom_point(aes(x=x,y=y), colour=kclusters$cluster) 

ggplot(data=wireless) +
  geom_point(aes(x=x,y=y)) +
  scale_fill_manual(kclusters$cluster)

cutoff = 68
# seems like 70 is a good cut off lets check how many points have more than 70
wireless_strong = wireless %>%
  mutate(S1 = S1 > -cutoff) %>% 
  mutate(S2 = S2 > -cutoff) %>% 
  mutate(S3 = S3 > -cutoff) %>% 
  mutate(S4 = S4 > -cutoff) %>% 
  mutate(S5 = S5 > -cutoff) 
# seems like 70 is not a good cutoff as we think
table(apply(wireless_strong[,3:7], 1, sum))

  0   1   2   3 
 19 150  80   5 

bad_locations = wireless_strong[as.numeric(apply(wireless_strong[,3:7], 1, sum)) < 2,]

plot(x=bad_locations$x, y=bad_locations$y, ylim=c(0,150), xlim=c(0,230))
points(x=AP$x,y=AP$y, col="red", cex=5)

View(data.frame(table(wireless$y)))